Which of these fractions is the smallest?

Cross-multiplying is quicker than a common denominator: for 22/29 against 13/17, $22\times 17=374$ while $13\times 29=377$, so 22/29 is smaller. As decimals, 22/29 ≈ 0.759, 13/17 ≈ 0.765, 17/22 ≈ 0.773 and 9/11 ≈ 0.818, confirming 22/29 is least.